1. Field of Invention
The present invention relates to an improved method for determining the pressure of fluid contained in a sedimentary rock. A mineralogically general force balanced stress/strain--loading limb relationship is a starting point. This relationship is defined in U.S. Pat. No. 5,282,384 to Holbrook, assigned to the assignee of the present invention, and which is incorporated herein by reference, which discloses how to calculate sedimentary rock pore pressure when the effective stress load is either constant or increasing and also teaches how the minimum principal stress and fracture pressure also can be calculated from in situ strain data in Normal Fault Regime .about.biaxial basins. Fracture pressure and pore fluid pressure are the safe force balance borehole fluid pressure limits for drilling the uncased (open to the surface) portion of a borehole into the subsurface.
Well after these loading limb open borehole force balance relationships were disclosed in the prior Holbrook patent, an extended set of force balanced Earth in situ stress/strain inter-relationships was discovered. These Earth in situ force balance inter-relationships can be applied to further improve the drilling decision making process. This newly discovered Earth in situ force balance inter-relationship, led to a direct force balance means of determining the physical location and pressure upper limit of fluid expansion generated pore fluid pressure. The methods disclosed in this invention produce further valuable geological information from in situ petrophysical measurements which is useful in the hydrocarbon recovery industry.
2. Background
Pore fluid pressure and fracture pressure are the most important external geologic factors affecting the safety and cost of drilling of an oil well. Exceeding either in situ force balance limit in an open borehole frequently leads to dangerous and usually costly well control problems. The borehole fluid hydrostatic pressure (Pb) must be greater than the formation pore fluid pressure (P.sub.p) if one is to avoid the risk of a possibly catastrophic blowout. Likewise, the borehole fluid circulating pressure must be less than the fracture propagation pressure (Pf) if one is to avoid the risk of lost circulation.
Several expensive casing strings are usually required so that an oil well can be drilled within the limits of the open borehole pore fluid pressure and fracture propagation pressure limits. Great savings would be realized during well planning if one or more casing string could be eliminated through better pore pressure and fracture pressure knowledge. The present invention also enhances the safety of oil or gas well drilling operations. Presently, a considerable portion of expensive rig time is spent in a remedial fashion dealing with unexpected pore pressure and fracture pressure problems encountered while drilling. The improved information from this invention should significantly reduce drilling operations costs by reducing the number of these dangerous situations.
Because of the critical relationship to drilling operations, there are numerous techniques for calculating pore fluid pressure. All known petrophysical prior art methods calculate pore fluid pressure indirectly based upon measured rock properties. Most of these methods follow a calibration procedure which is not based on mechanical or physical information. Instead, these calibration procedures are generally based upon the extension of an observed empirical relationship between a measured physical parameter and a "normal" or hydrostatic compaction trend. The empirical "normal" trend line (Pn) is the average value of the measured parameter which changes as a function of depth.
The change in the measured parameter (Pn) as a function of depth according to these prior art techniques is indirectly related to a change in compaction of the sedimentary rock. The measured parameter described in a pressure prediction technique is usually not compactional strain. The method operator in charge of pore pressure prediction must then decide whether the extrapolated "normal" compaction vs. depth trend line being used is correct or not using some non-physical interpretive basis. Direct empirical (i.e. non-physical) relationships have been the only pore pressure prediction techniques used by the oil industry until very recently.
Sedimentary rocks are compacted by the effective stress applied to their grain matrix framework. When fluid pressure is approximately hydrostatic and the overburden is gradually increasing, both depth and effective stress are increasing. Under these conditions, depth behaves as a pseudo-stress variable. However, when pore pressure is elevated, effective stress and overburden gradients can be either increasing or decreasing and depth is not a pseudo-stress variable.
Most of the prior art methods for determining pore fluid pressure use depth as a pseudo-stress variable in both "normal" and "excess" pressured intervals which results in significant pore pressure calculation errors. The potential for this error when using a non-physical velocity-depth trend line method will be illustrated later in reference to the patents to Kan et al.
Another significant failing of most prior art pore pressure calculation techniques is attributable to their basic formulation. According to prior art depth trend techniques, pore pressure (P.sub.p) is calculated as a sum of "normal" hydrostatic fluid pressure which is inferred from an extended compaction-depth trend; plus a differential or "excess" fluid pressure (.DELTA.P) which is related to a measured difference from the "normal" trend. The (.DELTA.P) calibration or correction term is back calculated after the fact from measured pore pressures in a nearby well or group of wells within a local area. The equation expressing this non-physical local calibration relationship is: EQU Pp=Pn+.DELTA.P (1)
where Pp is the pressure of fluid in the pore space of rock, Pn is the empirical calculation of the normal pressure trend line and .DELTA.P is the difference in pressure from the normal pressure trend line.
Equation (1) is not a physically representative mathematical formulation. Pascal's Principle requires that all of the fluids in a given local pore space or container be at the same pressure. Physically speaking, "excess" pressure cannot and does not exist in a pore space. Since the "excess" pressure term (.DELTA.P) does not exist in nature, "excess" pressure cannot be physically related to any measured parameter. Calibrating a measured physical parameter to a quantity which does not exist, i.e. (.DELTA.P), has been an acceptable engineering shortcut for a long time. The penalty when applying this (Pp=Pn+.DELTA.P) shortcut method is that the results are specific to the calibration area and the fluid pressurization mechanism in that particular field or reservoir. "Normal compaction trend" operators usually do not know the fluid pressurization mechanism, nor can they change their procedure to account for the mechanism. The (.DELTA.P) calibration is fundamentally non-physical and not related to the known loading and unloading stress/strain relationships of sedimentary rocks. As these stress/strain relationships are so different, there is great risk in mis-applying an empirical (Pp=Pn+.DELTA.P) relationship which contain no means of determining stress paths.
U.S. Pat. No. 5,081,612 to Scott et al discloses a method for determining formation pore pressure from remotely sensed seismic data. This particular method depends upon a hydrostatically compacted reference velocity vs. depth (Pn) profile. Referring back to Equation 1, this profile is essentially an observed or inferred curved (Pn) velocity gradient. The Scott et al pore pressure gradient technique applies to shale, which is also common to most of the prior art methods using a (Pp=Pn+.DELTA.P) formulation. Pore pressures are calculated with respect to the reference velocity vs. depth trend line which is an indirect violation of Pascal's Principle.
In U.S. Pat. Nos. 5,130,949 and 5,233,568 to Kan et al, like U.S. Pat. No. 5,081,612 to Scott et al, the basic pore pressure prediction method is also based upon a velocity vs. depth compaction trend line. Kan et al's FIG. 5 demonstrates the historically common but physically incorrect (Pp=Pn+.DELTA.P) methodology. The normal compaction trend line interpreted from the hydrostatic zone is shown on FIGS. 5b and 5d. The lowest hydrostatically compacted data point is slightly above 5,000 feet. The extrapolated (Pn) interval transit time-depth trend line decreases by half continuously every 8,000 feet on the logarithmic transit time scale shown.
The extrapolated empirical (Pn) shale transit time--depth trend line is beyond any possible physical reality at 8,000 feet or essentially 3,000 feet into the overpressured zone. Shales can compact no further than zero porosity which corresponds to a transit time of about 90 microseconds/foot. In regions that are more nearly hydrostatic than the example shown in reproduced FIG. 5, the 90 microseconds/foot shale transit time limit is not reached at depths above 20,000 feet.
The calibration within the (Pn) hydrostatic zone above 5,000 feet is reasonable. The projection to 90 microseconds/foot 3,000 feet below top of overpressure is physically unreasonable. Quartz is the most compaction resistant sedimentary mineral. The extrapolated (Pn) trend passes the zero porosity quartz transit time of 56 microseconds/foot at about 14,000 feet. The transit time of the Mohorovic discontinuity below the base of the Earth's crust is about 37 microseconds/foot. The (Pn) trend line is 37 microseconds/foot at 19,000 feet and continues to increase below. The actual depth of the base of the crust is about 100,000 feet on average, not 19,000 feet which is extrapolated from the interpreted normal shale compaction (Pn) depth trend of FIG. 5 of Kan et al.
The extrapolated (Pn) trend is grossly off compared to known transit time limits below the hydrostatic zone. Applying the (Pp=Pn+.DELTA.P) methodology the known error in the projected (Pn) depth trend is forced into the (.DELTA.P) term which is calculated by difference. Thus, the physically unreasonable (Pn) trend is automatically compensated for by the physically invalid (Pn+.DELTA.P) formulation relied upon for calibration. In fact any combination of (Pn+.DELTA.P) is forced to the correct answer by the measured pore pressure (Pp) in a calibration well. It takes two equal and opposite wrongs; one physically unrealistic (Pn), and one physically invalid (.DELTA.P) to make a right (Pp). Whenever the extrapolated (Pp=Pn+.DELTA.P) trend line methodology is reported to have been successfully applied; it signifies only that a force balance (.DELTA.P) correction has been applied to a frequently erroneous extrapolated (Pn) trend line.
All of the extrapolated (Pp=Pn+.DELTA.P) trend line methods suffer from the same non-physical (Pn) extrapolation which is transparent to the operator after the local calibration is made. The calibrations have only local applicability because you get a different extrapolated (Pn) trend depending upon where the base of the hydrostatically compacted depth interval occurs. In any particular area many other physical factors, for example overburden gradient, that exist affect the empirical calibration at that depth but are not accounted for in the empirical short cut methodology.
There are at least three (3) prior art methods for determining pore fluid pressure from petrophysical measurements which are based upon the effective stress law. A one-dimensional gravitational force balance was elucidated by Terzaghi, in his 1941 article entitled "Undisturbed Clay Samples and Undisturbed Clays", discussing compaction studies of marine sediments. Terzaghi first presented this uniaxial force balance equation; EQU Pp=S.sub.v -.sigma..sub.v ( 2)
This relationship states that the fluid pressure in the pore space (Pp) can be calculated as the difference between the overburden load (Sv) and the vertical load borne by the sediment grain--grain contacts (.sigma..sub.v). In the science of rock and soil mechanics, this (.sigma..sub.v) term is known as the effective vertical stress.
U.S. Pat. No. 5,200,929 to Bowers is based upon in situ empirically determined velocity vs. calculated effective stress relationships. It uses the Terzaghi uniaxial Equation (2) to calculate effective stress. In NFR.about.biaxial basins the uniaxial calibration is coincidentally related to average effective stress force balance which directly causes the observed sediment compaction. This method accounts for both the loading and unloading stress/strain relationships of sedimentary rocks. The method is intended for use only in velocity reversal zones where fluid expansion unloading is the known fluid pressurization mechanism. The method is dependent only on velocity measurements which are indirectly related to strain and lithology.
The Bowers method is a significant technical advance because it uses a uniaxial approximate measure of effective stress and for its recognition of stress/strain hysteresis in sedimentary rocks. However, like the previously described pore pressure methods, the Bowers method also depends upon local empirical-velocity calibration to determine the coefficients for all its calibration and pore pressure prediction relationships.
Using in situ velocity vs. effective stress data for shales only, Bowers describes a method for defining the shape of loading and unloading effective stress-shale acoustic velocity curves. His "virgin curve relationship" is portrayed as the solid line on Bower's FIG. 4. This curve corresponds to a loading limb stress/strain relationship with shale velocity being the indirect measure of strain.
At present the shale velocity-strain relationship is still poorly known. The velocity of an individual shale sample varies by up to 25% depending on whether the measurement is made parallel or perpendicular to bedding, as discussed in a 1994 article by Sayers, entitled "The Elastic Anisotropy of Shales". An in situ measurement of velocity on shales with identical strain would produce very different pore pressure answers depending on the formation dip at the measurement location.
FIG. 4 of the Bowers patent shows how the extension of local empirical velocity loading limb and unloading limb relationships intersect. The position of this intersection point in both depth and effective stress space has a major impact on the value of the unloading limb calculated pore pressure. The data from both loading and unloading limbs must be known and their curving functions determined through interpolation before their intersection point can be determined by extrapolation. No other means for establishing the onset of unloading limb pore pressure is revealed by Bowers. If this method were to be applied with real-time Measurement-While-Drilling data, one would not have a criterion to determine where and when to switch from loading to unloading stress-velocity relationships.
U K Patent No. 2,174,201A to Fitzgerald reveals a common misunderstanding with respect to the interpretation of laboratory vs. in situ stress/strain relationships. Fitzgerald's method is based upon two (2) linear acoustic velocity vs. stress relationships observed in two (2) shales in a laboratory. Virtually all observed laboratory stress/strain relationships occur along the dominantly elastic unloading-reloading stress path of a rock sample. These rock specific stress paths intersect a mineralogy specific loading limb stress path at the point of maximum effective stress loading. There is no clear indication apparent during laboratory experiments on relatively hard rocks when or where the hysteresis join point is reached. The slopes of the initial loading vs. unloading-reloading limbs are very different.
Fitzgerald's patent indicates a lack of awareness of stress/strain hysteresis in sedimentary rocks and makes calculations based only upon the unloading-reloading stress path. In Fitzgerald, the key rock description qualifier "known constitution" is entirely appropriate and correct. For this method to operate as described a huge catalog of "known constituent" sedimentary rocks would have to be provided to appropriately match stress paths. Only two (2) rock stress paths are described. Fitzgerald describes three (3) empirical stress path coefficients which would need to be established to have a predictive equation. These coefficients could not be established without the "known constituent" rock sample or its equivalent from a rock sample catalog. The Fitzgerald patent is operative only for the two (2) rocks described and could not be generalized into a general subsurface pore pressure predictive method.
U.S. Pat. No. 5,282,384 to Holbrook applies force balance for pore pressure prediction using a power law effective stress/strain compaction function. The key scientific elements to this methodology and approach are:
1. The use of the uniaxial Terzaghi force balance (Equation 2) in .about.biaxial Normal Fault Regime Basins. PA1 2. The correlation of effective stress to solidity (1.0-.phi., where .phi. is porosity) which is a direct measure of in situ strain for granular solids. One skilled in the art will recognize the substitution of the relationship (.phi./1.0-.phi.). PA1 3. The discovery through this application that both vertical effective stress and the effective horizontal/vertical stress ratio in .about.biaxial Normal Fault Regime basins are directly related to in situ strain in all lithologies and at all depths.
These direct stress/strain relationships are related to sedimentary rock mineralogy and expressed quantitatively as Equations 6, 7, and 8 in the Holbrook Pat. No. 5,282,384. These equations and empirical coefficients describe a complete three-dimensional grain and fluid force balance. Additionally, the equations in the patent explain why and how the uniaxial Terzaghi force balance works in .about.biaxial Normal Fault Regime basins where horizontal effective stresses are known to increase with depth. Further, lithologic and stress technical support for the patented method are described in articles by Holbrook in 1995, "The Relationship Between Porosity, Mineralogy, and Effective Stress in Granular Sedimentary Rocks", and 1996, "The Use of Petrophysical Data for Well Planning, Drilling Safety and Efficiency" and "A Simple Closed Force Balanced Solution for Pore Pressure, Overburden, and the Principal Effective Stress in the Earth".
There are severe calibration problems with all of the (Pp=Pn+.DELTA.P) prior art empirical pore pressure prediction methodologies described above. Most of the prior art acoustic pore pressure prediction methodologies use the same non-physical relationship (Equation 1) and suffer the same general pore pressure calibration-prediction problems. The calibrations for all these methods, even including Bowers' (Equation 2) empirical effective stress-velocity relationships apply only locally. The fundamental problem with all the other prior art methods is that of the unspecified relationships between stress and strain. Holbrook (Equation 2) is the only prior art pore pressure method which embodies a direct physical in situ stress/strain calibration basis.
Articles by Ward et al in 1994, "The Application of Petrophysical Data to Improved Pore and Fracture Pressure Determination in North Sea Graben HPHT Wells", and 1995, "Evidence for Sedimentary Unloading caused by Fluid Expansion Overpresssure-generating Mechanics", point out evidence for fluid expansion generated fluid overpressuring which was directly related to in situ measurable strain (solidity). The unloading limb stress/strain (solidity) data plotted in a very different areas are in general agreement with Bowers' "virgin curve" vs. unloading velocity data. Ward et al's FIG. 2 from their 1994 article illustrates the similarities, differences, advantages and implementation problems associated with applying unloading stress/strain relationships to the problem of pore pressure determination.
The Ward et al FIG. 2 loading and unloading limb relationships are power law linear stress/strain functions. The major significant advantages of this over the Bowers calibration are that: 1) effective stress is directly related to in situ strain; and 2) the power law function is linear, not curved, which makes calibration, interpolation and extrapolation much more simple and reliable. FIG. 4 of Bowers and FIG. 2 of Ward et al are geometrically similar. Bowers' shale velocity curves would approximate Ward et al's power law linear stress/strain functions if the appropriate material properties transformations were made. The interpretation calibration step and the pore pressure prediction step are much easier to accomplish and more accurate when using the force balanced power law linear relationships.
Ward et al points out in their FIG. 3 that there are many possible unloading stress/strain relationships related to the loading limb relationship depending on the last peak effective stress loading. The interpretive definition of this loading limb intersection point is a critical problem here as it was in the Bowers' methodology.
Ward et al, in the 1994 article, made some observations which are illustrated as FIGS. 3 and 4 which are coincidentally related to a physical rock properties means of determining the loading vs. fluid expansion unloading intersection point in the subsurface. The depth range of a low porosity vertical seal is shown on the FIG. 3 geologic cross section. Pore fluid pressure gradient as indicated by the heavy curved lines on the figure increases dramatically somewhere within the low porosity seal zone. The onset of fluid expansion unloading probably occurs somewhere in the low porosity seal zone which can be recognized from petrophysical measurements. This relationship is discerned mainly by inference from the markedly different observed pressure gradients above and below the low porosity seal zone. Low porosity is a property of the seal zone, but it does not capture or quantify the actual pressure seal relationship.
Ward et al's 1994 article FIG. 5 is a generalized pressure profile showing the relationships between disequilibrium compaction fluid pressurization mechanisms and fluid expansion pressurization mechanisms. The low porosity vertical seal within the chalk is also shown on this diagram. Supporting this circumstantial evidence are the calculations of which indicated that a very low permeability seal is needed for the fluid expansion pressurization mechanism to be operative.
Gaarenstroom et al, in a 1993 article entitled "Overpressures in the Central North Sea: Implications for Trap Integrity and Drilling Safety", also demonstrate a reasonable partial understanding of the relationships that govern pore fluid pressure in the subsurface. Gaarenstroom et al relate trap integrity to formation strength. While a certain minimum formation strength is required, it is not strength that is regulating the compartment pressure. Very weak shales, salt, as well as very strong impermeable quartzites have very different strengths. All these different strength lithologies can equally well accomplish the job of sealing a pressure compartment as long as they have sufficiently low intergranular permeability.
FIGS. 3 and 4 of the Ward et al 1994 article show the transition between loading and unloading limb stress/strain relationships is related to a low porosity zone within the North Sea chalk interval. The transition between effective stress loading and unloading occurs in this zone. The zone definition is broad and general and does not specify the sealing mechanism or exactly where the seal is located within the low porosity zone. The difference between Ward et al's description and the present invention is that low porosity is coincident with, but is not equal to high fracture pressure. A low porosity rock will have different fracture pressures which also depend upon vertical effective stress and pore pressure. Fracture pressure is the actual force that holds the in situ Compartment Pressure Limit Valve closed.
Ward et al and Gaarenstroom et al have identified two (2) different factors, strength and low porosity which are coincidentally related to fracture pressure under special circumstances. Methods related to these parameters should work in a relative sense under the particular geologic situation they describe. The distinction made here is that when fracture pressure is used as the discrimination parameter, the method works in general because of force balance regardless of these other circumstances.
The relationships described by Gaarenstroom et al, Bowers and Ward et al indicate that they have a general understanding of the factors coincidentally related to the occurrence of pressure compartments, and loading vs. unloading stress/strain relationships. The caprock seal required for unloading can be recognized as a relative porosity low within a sequence as described by Ward et al. Porosity provides a means for recognizing a compartment pressure seal under the specified average regional conditions. But porosity does not provide the means for quantifying the caprock's pressure sealing capacity which controls the pore pressure below.
Seal pressure capacity is the truly important aspect of pore pressure forecasting ahead of the bit. Gaarenstroom et al describe rock strength relationship is likewise a related seal recognition criteria which lacks the means for seal capacity quantification. The solution to these problems lies in the seal mechanism which is not identified in the prior art.